Let {xn} be the sequence defined recursively by X1 = 2 and 5 Xn+l = 2 + Xn for all n Z 1. Prove that {xn} converges and find the limit of the sequence.

Answer:

7.89 x 10<superscript=10>

Step-by-step explanation:

Answer:

x = 60°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6, thus

sum = 180° × 4 = 720°

Each interior angle = 720° ÷ 6 = 120°

interior angle + exterior angle = 180°, that is

120° + x = 180° ( subtract 120° from both sides )

x = 60°

SOLUTION:

Step 1:

In this question, we are given the following:

The equation of the directrix for the parabola:

Step 2:

The details of the solution are as follows:

Next, we can see that the equation of the directrix for the parabola is at:

This is because:

Then, y = k - p

y = 3 - p

p = 1/ 4a

p = 1 / 4(-1/8)

p = -2

y = 5

The corresponding heap structure for the array a = (5, 7, 4, 3, 1, 2, 6) is as shown above.

To represent a heap structure corresponding to the array a = (5, 7, 4, 3, 1, 2, 6), we will use a binary heap. In a binary heap, the elements are arranged in a way that satisfies the heap property.

The heap property states that for a binary max heap, each parent node has a value greater than or equal to its children, while for a binary min heap, each parent node has a value less than or equal to its children.

Using the given array, we can build a binary max heap as follows:

Step 1: Start with the array a.

5, 7, 4, 3, 1, 2, 6

Step 2: Rearrange the elements to satisfy the heap property.

     7

   /   \

  5     6

 / \   / \

3   1 2   4

In this representation, the topmost element, 7, is the root of the heap. Each parent node is greater than or equal to its children.

Therefore, the corresponding heap structure for the array a = (5, 7, 4, 3, 1, 2, 6) is as shown above.

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Answer:

72°

Step-by-step explanation:

here's your solution

=> we know angle A + angle S = 2

=> angle 2 = 30° + 42°

=> 72°

hope it helps

The archway is about 20.8 meters wide at ground level.

We can start by using the formula for a parabolic archway:

y = a\((x-h)^{2}\) + k

where y is the height, x is the width at a certain height, h is the horizontal distance from the vertex to the center of the archway, k represents the height of the vertex, and a determines the shape of the parabola.

We know that the archway is 12 meters high at the vertex, so we can plug in the values we have:

12 = a\((0-h)^{2}\) + k

12 = a\(h^{2}\) + 12

Simplifying this equation, we get:

a = -1/(4h)

We also know that at a height of 10 meters, the width of the archway is 8 meters. Plugging in these values:

10 = a\((4-h)^{2}\) + 12

10 = -1/(4h)\((16-8h)^{2}\) + 12

Simplifying this equation, we get a quadratic equation in terms of h:

0 = 2\(h^{2}\) - 3h - 14

h = 2 or h = -7/2

Since h represents a distance, it cannot be negative, so we take h = 2.

Now we can find the width of the archway at ground level (where y = 0):

0 = a\((x-2)^{2}\) + 12

-a\((x-2)^{2}\) = 12

-a = 12/\((x-2)^{2}\)

Putting our value for a, we get:

1/(4h) = 12/\((x-2)^{2}\)

Solving for x, we get:

x = 20.8 meters

Therefore, the archway is about 20.8 meters wide at ground level.

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To simplify the expression cot(x)sin(x) - sin(x) + cos(x), we can combine like terms and factor out sin(x) with the help of trigonometric identity.

From the given expression:

cot(x)sin(x) - sin(x) + cos(x) = sin(x)(cot(x) - 1) + cos(x)

This expression can be simplified further by using the trigonometric identity cot(x) = cos(x)/sin(x):

sin(x)(cot(x) - 1) + cos(x) = sin(x)(cos(x)/sin(x) - 1) + cos(x)

Now, we can simplify the expression by canceling out sin(x) in the numerator and denominator:

sin(x)(cos(x)/sin(x) - 1) + cos(x) = cos(x) - sin(x) + cos(x)

Finally, we can combine like terms:

cos(x) - sin(x) + cos(x) = 2cos(x) - sin(x)

Therefore, the simplified expression is 2cos(x) - sin(x).

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Answer:

4.

Step-by-step explanation:

To find the area of one square base of a right prism, you need to determine the length of one side of the square and then multiply it by itself (i.e., square it).

For example, if the length of one side of the square base is 5 cm, then the area of the square base is 25 cm² (i.e., 5²). This is because the area of a square is calculated by multiplying its length by its width, and since all sides of a square are equal, you only need to square one side to get its area.

Therefore, to find the area of one square base of a right prism, you need to know the length of one side of the square.

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Answer:

reference attached

hope it helps you <3

The strategy that can be used to prove that the diagonals of a parallelogram bisect each other is congruent triangles .

Given :

Let ABCD is a parallelogram with midpoint M .

To prove that he diagonals of a parallelogram bisect each other we have to go through the following steps:

Angle DBA is congruent to angle BDC.

Angle CMD is congruent to angle AMB.

Triangle CMD is congruent to triangle AMB.

Segment AM is congruent to segment MC.

M is the midpoint of segment AC.

Segment BD bisects segment AC.

Segment BM is congruent to segment MD.

M is the midpoint of segment BD.

Segment AC bisects segment BD.

Hence we have to use the concept of congruent triangles in order to prove that the diagonals of a parallelogram bisect each other.

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By doing a simple change of units, we will get:

a) 144km

b) 96km

c) 200km

First, we know that 5 miles is equivalent to 8 kilometers, then we can write:

5 mi = 8km

1 = (8km/5mi)

Now, remember that if we multiply by 1 the value does not change, then if we multiply by  (8km/5mi) (which is equivalent to 1) we don't change the value, only the units (from miles to km).

a) According to the table, the distance between Kendal and York is 90mi, then the distance in kilometers is:

d = 90 mi = (90mi)*(8km/5mi) = 144km

b) Between Sheffield and york there are 60 miles, then the distance is just:

D = 60mi = (60mi)*(8km/5mi) = 96 km

c) Between Lincoln and Middlesbrough there are 125 miles, then the distance in kilometers is:

d = 125mi = (125 mi)*(8km/5 mi) = 200km

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The Z score that is equivalent to the raw score 92.5 is B. -1.25.

A Z score represents the number of standard deviations a raw score is from the mean in a normal distribution. To calculate the Z score, we use the formula: Z = (X - μ) / σ, where X is the raw score, μ is the mean, and σ is the standard deviation.

Given that the mean score is 100 and the standard deviation is 15, we can calculate the Z score for the raw score 92.5 as follows:

Z = (92.5 - 100) / 15

Z = -7.5 / 15

Z = -0.5

Therefore, the Z score that is equivalent to the raw score 92.5 is -0.5.

The Z score is a useful measure in statistics that allows us to standardize and compare data points across different distributions. It helps us understand the relative position of a data point within a distribution and determine how unusual or typical that data point is compared to others. By calculating the Z score, we can easily determine the percentage of data points that fall below or above a particular value in a normal distribution, which aids in making statistical inferences and drawing conclusions.

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The sampling distributions are used for statistical tets.

Hence,The sampling distributions are used for statistical tets.

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Answer:

-9 is a rational number and an integer.  

Step-by-step explanation:

A rational number is any number that can be expressed as a fraction. -9 can be written as \(-\frac{9}{1}\), thus it is a rational number.  

A whole number is a number that is not negative and does not have fractions or decimals. -9 is negative, thus it is not a whole number.

An integer is a number with no fractions or decimals, but it can be negative or positive. -9 meets these requirements, thus it is an integer.

An irrational number is a number that cannot be written as a fraction. Irrational numbers are not rational. Thus, -9 is not an irrational number.

So, -9 is a rational number and an integer.  

Answer:

x= 180 degrees

Step-by-step explanation:

b longest side

The area of the shaded region of this figure which can be calculated by the difference of the larger region from the smaller region would be 104 in.²

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Area of a larger rectangle

= Length × Width

= 18 × 12

= 216 in.²

Area of the smaller rectangle

Length = 12 - 2 - 2 = 8 in.

Width = 18 - 2 - 2 = 14 in.

= Length × Width

= 8 × 14

= 112 in.²

Area of the shaded region = Area of a larger rectangle - Area of the smaller rectangle

= 216 - 112

= 104 in.²

Hence, the area of the shaded region of this figure is 104 in.²

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Answer:

9/100

Step-by-step explanation:

% = over 100

9% = 9/100

Answer:

9/100

Step-by-step explanation:

The value of y will be;

⇒ y = 7.68

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In a triangle,

Perpendicular distance = y

Hypotenuse = 10

Now,

Since, We know that;

⇒ sin θ = Perpendicular / Hypotenuse

Substitute all the values, we get;

⇒ sin θ = Perpendicular / Hypotenuse

⇒ sin 48° = y / 10

⇒ 0.768 = y/10

⇒ y = 0.76 x 10

⇒ y = 7.68

Thus, The value of y will be;

⇒ y = 7.68

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All solutions to the given system of congruences are given by (x \equiv 1 \mod 60), (x \equiv 3601 \mod 60), and so on, where the difference between consecutive solutions is a multiple of 60.

To find all solutions to the system of congruences:

(x \equiv 1 \mod 3),

(x \equiv 2 \mod 4),

(x \equiv 2 \mod 5),

we can use the Chinese Remainder Theorem.

The Chinese Remainder Theorem states that if we have a system of congruences (x \equiv a_1 \mod n_1), (x \equiv a_2 \mod n_2), ..., (x \equiv a_k \mod n_k) with pairwise coprime moduli ((n_i) and (n_j) are coprime for (i \neq j)), then there exists a unique solution modulo (N = n_1 \cdot n_2 \cdot ... \cdot n_k).

In our case, the moduli are 3, 4, and 5, which are pairwise coprime. Thus, the modulus (N = 3 \cdot 4 \cdot 5 = 60).

We can express each congruence in terms of the modulus (N) as follows:

(x \equiv 1 \mod 3) can be written as (x \equiv -59 \mod 60),

(x \equiv 2 \mod 4) can be written as (x \equiv -58 \mod 60),

(x \equiv 2 \mod 5) can be written as (x \equiv -58 \mod 60).

Now, we can apply the Chinese Remainder Theorem to find the unique solution modulo 60.

Let's denote the solution as (x = a \mod 60).

Using the first congruence, we have (a \equiv -59 \mod 60). This implies that (a = -59 + 60k) for some integer (k).

Substituting this into the second congruence, we have (-59 + 60k \equiv -58 \mod 60).

Simplifying, we get (k \equiv 1 \mod 60).

Therefore, the general solution is (x \equiv -59 + 60k \mod 60) where (k \equiv 1 \mod 60).

To find all solutions, we can substitute different values of (k) satisfying (k \equiv 1 \mod 60) and calculate the corresponding values of (x).

For example, when (k = 1), we get (x \equiv -59 + 60(1) \equiv 1 \mod 60).

Similarly, when (k = 61), we get (x \equiv -59 + 60(61) \equiv 3601 \mod 60).

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Answer:

The area is 154 in square

153.9380400

Hope this helps :T

Answer:

I'll write something just to help that person be the brainliest

Step-by-step explanation:

Cross-sectional data refers to data collected from a group of participants at a particular point in time. It provides information about one or more variables of interest that can be used to draw conclusions about the population as a whole.

Examples of cross-sectional data include the test scores of students in a class, the current average prices of regular gasoline in different states, and the sales prices of single-family homes sold last month in California.Therefore, option D) All of the Answers are examples of cross-sectional data.

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Step-by-step explanation:

I hope the answer helps u dear

Answer:

\(a^3-b^3+4a-4b:\:\left(a-b\right)\left(a^2+ab+b^2+4\right)\)

Step-by-step explanation:

Given the expression

\(a^3-b^3+4a-4b\)

solving the expression

\(a^3-b^3+4a-4b\)

as

\(\mathrm{Apply\:Difference\:of\:Cubes\:Formula:\:}x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)\)

\(a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\)

also

\(\mathrm{Factor\:out\:common\:term\:}4\)

\(=4\left(a-b\right)\)

so the expression becomes

\(=\left(a-b\right)\left(a^2+ab+b^2\right)+4\left(a-b\right)\)

\(\mathrm{Factor\:out\:common\:term\:}\left(a-b\right)\)

\(=\left(a-b\right)\left(a^2+ab+b^2+4\right)\)

Therefore,

\(a^3-b^3+4a-4b:\:\left(a-b\right)\left(a^2+ab+b^2+4\right)\)

Answer:

a

Step-by-step explanation:

Answer:

-7x²-13x+2

Step-by-step explanation:

-7x²-14x+1x+2

Answer:

x = 4

Step-by-step explanation:

3x = 12, x = 4. I took algebra 1 and 2